Math / Algebra

Question\begin{align} 2x &= 4 + 2 \\ 1 + X Y \end{align}

Studdy Solution

STEP 1

1. The problem involves solving a system of linear equations.
2. The system of equations is given as: - $x = y + 2$ - $1 + x = y$
3. We need to find the values of $x$ and $y$ that satisfy both equations simultaneously.

STEP 2

1. Understand the given equations.
2. Substitute one equation into the other to eliminate one variable.
3. Solve for the remaining variable.
4. Substitute back to find the other variable.
5. Verify the solution by substituting both values back into the original equations.

STEP 3

The given equations are:
1. $x = y + 2$
2. $1 + x = y$
These are two linear equations in two variables, $x$ and $y$ .

STEP 4

Substitute the expression for $x$ from the first equation into the second equation:
Since $x = y + 2$ , substitute into $1 + x = y$ :
$1 + (y + 2) = y$

STEP 5

Simplify the equation:
$1 + y + 2 = y$
$3 + y = y$

STEP 6

Subtract $y$ from both sides to isolate the constant:
$3 = 0$
This is a contradiction, indicating that there is no solution to the system of equations.

STEP 7

Since we reached a contradiction, the system of equations has no solution. The lines represented by these equations are parallel and do not intersect.

Was this helpful?

Question\begin{align} 2x &= 4 + 2 \\ 1 + X Y \end{align}

Studdy Solution

STEP 1

1. The problem involves solving a system of linear equations.
2. The system of equations is given as: - $x = y + 2$ - $1 + x = y$
3. We need to find the values of $x$ and $y$ that satisfy both equations simultaneously.

STEP 2

1. Understand the given equations.
2. Substitute one equation into the other to eliminate one variable.
3. Solve for the remaining variable.
4. Substitute back to find the other variable.
5. Verify the solution by substituting both values back into the original equations.

STEP 3

The given equations are:
1. $x = y + 2$
2. $1 + x = y$
These are two linear equations in two variables, $x$ and $y$ .

STEP 4

Substitute the expression for $x$ from the first equation into the second equation:
Since $x = y + 2$ , substitute into $1 + x = y$ :
$1 + (y + 2) = y$

STEP 5

Simplify the equation:
$1 + y + 2 = y$
$3 + y = y$

STEP 6

Subtract $y$ from both sides to isolate the constant:
$3 = 0$
This is a contradiction, indicating that there is no solution to the system of equations.

STEP 7

Since we reached a contradiction, the system of equations has no solution. The lines represented by these equations are parallel and do not intersect.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question\begin{align*} 2x &= 4 + 2 \\ 1 + X Y \end{align*}

Studdy Solution

STEP 1

1. The problem involves solving a system of linear equations.2. The system of equations is given as: - x=y+2 x = y + 2 x=y+2 - 1+x=y 1 + x = y 1+x=y3. We need to find the values of x x x and y y y that satisfy both equations simultaneously.

STEP 2

1. Understand the given equations.2. Substitute one equation into the other to eliminate one variable.3. Solve for the remaining variable.4. Substitute back to find the other variable.5. Verify the solution by substituting both values back into the original equations.

STEP 3

The given equations are:1. x=y+2 x = y + 2 x=y+22. 1+x=y 1 + x = y 1+x=yThese are two linear equations in two variables, x x x and y y y.

STEP 4

Substitute the expression for x x x from the first equation into the second equation:Since x=y+2 x = y + 2 x=y+2, substitute into 1+x=y 1 + x = y 1+x=y:1+(y+2)=y 1 + (y + 2) = y 1+(y+2)=y

STEP 5

Simplify the equation:1+y+2=y 1 + y + 2 = y 1+y+2=y3+y=y 3 + y = y 3+y=y

STEP 6

Subtract y y y from both sides to isolate the constant:3=0 3 = 0 3=0This is a contradiction, indicating that there is no solution to the system of equations.

STEP 7

Since we reached a contradiction, the system of equations has no solution. The lines represented by these equations are parallel and do not intersect.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question\begin{align} 2x &= 4 + 2 \\ 1 + X Y \end{align}

1. The problem involves solving a system of linear equations.
2. The system of equations is given as: - $x = y + 2$ - $1 + x = y$
3. We need to find the values of $x$ and $y$ that satisfy both equations simultaneously.

1. Understand the given equations.
2. Substitute one equation into the other to eliminate one variable.
3. Solve for the remaining variable.
4. Substitute back to find the other variable.
5. Verify the solution by substituting both values back into the original equations.

The given equations are:
1. $x = y + 2$
2. $1 + x = y$
These are two linear equations in two variables, $x$ and $y$ .

Substitute the expression for $x$ from the first equation into the second equation:
Since $x = y + 2$ , substitute into $1 + x = y$ :
$1 + (y + 2) = y$

Simplify the equation:
$1 + y + 2 = y$
$3 + y = y$

Subtract $y$ from both sides to isolate the constant:
$3 = 0$
This is a contradiction, indicating that there is no solution to the system of equations.